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Lesson 3.7 Solving Inequalities Using Multiplication or Division Objective: You will solve inequalities using multiplication or division so you can find measurements, as in Example 3.

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EXAMPLE 1 Solving an Inequality Using Multiplication Original inequality Multiply each side by –8. Reverse inequality symbol. Simplify. n ≤ –16 1 8 n ≥ 2 – –8 1 8 – n ≤ –8 2 1 8 n ≥ 2 –

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EXAMPLE 2 Solving an Inequality Using Division Original inequality Divide each side by –3. Reverse inequality symbol. Simplify. –5 < m 15 > –3m 15 –3 < –3m –3 15 > –3m

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EXAMPLE 3 Using the Division Property of Inequality Biology About 15,000 fruit-eating bats live on Barro Colorado Island. Yearly they eat up to 61,440,000 grams of fruit. Write and solve an inequality to find about how many grams g of fruit each bat eats yearly. SOLUTION

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EXAMPLE 3 Using the Division Property of Inequality Write an algebraic model. Divide each side by 15,000. Simplify. g ≤ 4096 15,000g ≤ 61,440,000 15,000g 15,000 ≤ 61,440,000 15,000 Each bat eats up to 4096 grams of fruit in a year. ANSWER

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GUIDED PRACTICE for Examples 1, 2, and 3 Solve the inequality. 1. t 6 > 4 Original inequality Multiply each side by 6. Simplify. t 6 > 4 1 6 > 4 6 t 6 t >24

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GUIDED PRACTICE for Examples 1, 2, and 3 Solve the inequality. 2. 1 2 – x ≤ 10 Original inequality Multiply each side by –2. Reverse inequality symbol. Simplify. 1 2 – x < 10 1 2 – x > 10–2 x> –20

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GUIDED PRACTICE for Examples 1, 2, and 3 Solve the inequality. 3. 27 > –3t Original inequality Divide each side by –3. Reverse inequality symbol. Simplify. 27> –3t 27–3t –3 < t < –9

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GUIDED PRACTICE for Examples 1, 2, and 3 Solve the inequality. 4. 9n < 63 Original inequality Divide each side by 9. Simplify. 9n < 63 9n9n63 9 9 < 7 < n

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GUIDED PRACTICE for Examples 1, 2, and 3 5. Fruit Bats A bat that weighs about 25 grams can eat up to 2.5 times its body mass in figs in one night. How many grams g of figs can it eat? A bat can eat figs < A bat weighs figs bat can eat in one night g < 25 2.5 Write an algebraic model. Multiply. g < 62.5 A bat can eat up to 62.5 g of figs. ANSWER

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